Simulation with model selection by BIC
1 Simulation set up
- Sample size for both training and testing set is 200
- 50 covariates, 10 groups, 5 covariates each group
- group 1 and 3 are important, with beta = c(1, 2, 3, 4, 5)
- signal-to-noise ratio = 1
- use BIC to select lambda
- use prediction error to evaluate prediction
- tuning parameter of weight: 0, .25, .5, .75, 1, no scale. just used cost for weight
- cost randomly generated with each simulation
- solution path
2 zero correlation for both inter and intra group
2.1 Results
## # A tibble: 5 x 3
## variable ave_pe med_pe
## <fct> <dbl> <dbl>
## 1 Lasso 1.22 1.21
## 2 CRL 1.23 1.21
## 3 GL 1.14 1.13
## 4 CGL 1.15 1.14
## 5 rCGL 1.13 1.13## # A tibble: 5 x 3
## variable ave_cpp med_cpp
## <fct> <dbl> <dbl>
## 1 Lasso 82.7 80.2
## 2 CRL 81.8 78.9
## 3 GL 64.5 62.3
## 4 CGL 61.8 60.3
## 5 rCGL 61.4 60.42.2 Solution path
3 zero between-group, 0.5 within group correlaion
3.1 Results
## # A tibble: 5 x 3
## variable ave_pe med_pe
## <fct> <dbl> <dbl>
## 1 Lasso 1.13 1.12
## 2 CRL 1.14 1.13
## 3 GL 1.13 1.12
## 4 CGL 1.14 1.14
## 5 rCGL 1.13 1.12## # A tibble: 5 x 3
## variable ave_cpp med_cpp
## <fct> <dbl> <dbl>
## 1 Lasso 49.9 45.3
## 2 CRL 51.4 46.3
## 3 GL 64.6 62.9
## 4 CGL 61.9 60.6
## 5 rCGL 62.2 61.13.2 Solution path
4 0.5 correlation for both between and within groups
4.1 Results
## # A tibble: 5 x 3
## variable ave_pe med_pe
## <fct> <dbl> <dbl>
## 1 Lasso 1.13 1.13
## 2 CRL 1.14 1.13
## 3 GL 1.14 1.14
## 4 CGL 1.16 1.16
## 5 rCGL 1.14 1.13## # A tibble: 5 x 3
## variable ave_cpp med_cpp
## <fct> <dbl> <dbl>
## 1 Lasso 117. 118.
## 2 CRL 105. 108.
## 3 GL 85.8 86.7
## 4 CGL 86.2 86.2
## 5 rCGL 80.7 79.84.2 Solution path
